Question

Please answer the following questions about paged memory...

A) How much space needs to be allocated in the minimum and maximum cases for a two-level page table for a machine with a 32-bit virtual memory address, a 1K page size, and which has four times as many inner pages as outer pages? Assume any stored page table value requires 32 bits.

B) For the two-level paging approach above, if a Translation Lookaside Buffer (TLB) is used and can cache both inner and outer page tables, write down the formula for the Effective Access Time (EAT) for a page reference assuming a hit rate of a, a TLB access time of 60 ns and a memory access time of 200 ns. What must a be for EAT=280 ns? Assume that either both page tables are in the TLB or neither are.

Answer 1

minimum case page offset = 1k = 2^10 bits outer P.T Inner POT Since, p + d = 32 p + 10 = 32 p = 22 Divide this 22 into 2 equal points of 11 bits each \r\n max_0 case 4 times entries in outer POT as compared to Inner POT. p_1 = 18(greater than 4 time) p_2 = 4 so, Inner PT requires 4 bits where as outer PT requires 18 bits. \r\n EAT = p * (page Fault) server time + (1 - p)X memory Access 280 = a times (60 + 200 + 200) + (1 - a) times (60 + 200) 280 = 460a + 260 - 260a 20 = 200a a = 20/200 = 0.1% TLB hit time = TLB search time + memory Access time TLB miss time = TLB search time + 2 * memory Access time